Set Theory and Interval Notation

Professor Dave introduces sets in algebra, covering domains of functions, interval notation, types of sets, and operations like intersection and union. He explains empty and null sets and demonstrates solving inequalities using sets.

What does the domain of a function represent?

• The set of all integers

• The set of all possible inputs

• The set of all real numbers

• The range of possible outputs

How is an open interval represented in interval notation?

• With square brackets

• With angle brackets

• With curly braces

• With parentheses

What does an open parenthesis in interval notation signify?

• A null set

• A union of sets

• Exclusivity

• Inclusivity

What is the union of two sets?

• The set of all elements in either set

• The set of elements in the first set only

• The set of elements in the second set only

• The set of elements common to both sets

What symbol represents the null set?

• An empty pair of brackets

• The Greek letter phi

• A zero

• A circle

In interval notation, what does a closed bracket indicate?

• Exclusivity

• Inclusivity

• Infinity

• A null set

What is the intersection of the set of odd natural numbers and the set of even natural numbers?

• The null set

• The set of all real numbers

• The set of all integers

• The set of all natural numbers

What is the solution to the inequality |X| > 2?

• The interval from -2 to 2

• The union of intervals from -∞ to -2 and 2 to ∞

• The interval from 2 to ∞

• The interval from -∞ to 2

How do you represent a system of inequalities using set theory?

• By listing all possible solutions

• By finding the intersection of the solution sets

• By using only open intervals

• By finding the union of the solution sets

What is the correct interval notation for X > -3 and X ≤ 4?

• [-3, 4]

• (-3, 4)

• [-3, 4)

• (-3, 4]